$A$ uniform rod of length $l$ is being rotated in a horizontal plane with a constant angular speed $\omega$ about an axis passing through one of its ends. If the tension generated in the rod due to rotation is $T(x)$ at a distance $x$ from the axis,then which of the following graphs depicts it most closely?

For every particle of a rigid body in rotational motion,which of the following is true?

Explain that angular velocity is a vector and its direction is given by the right-hand screw rule.

As shown in the figure,a small wheel is coaxially connected to a larger wheel of double its radius. The system rotates about a common axis. Strings $A$ and $B$ are attached to the wheels such that they do not slip. If $x$ and $y$ are the distances covered by $A$ and $B$ in the same time interval,then:

$A$ uniform solid cylinder of mass $M$ and radius $R$ rotates about a frictionless horizontal axle. Two similar masses $m$ are suspended with the help of two ropes wrapped around the cylinder. If the masses fall down through a distance $h$,the angular velocity of the cylinder will be

Two masses $m$ and $2m$ are connected by a light string passing over a pulley (disc) of mass $M = 30m$ and radius $r = 0.1 \ m$. The pulley is mounted in a vertical plane and is free to rotate about its axis. The $2m$ mass is released from rest. Find its speed when it has descended through a height of $h = 3.6 \ m$. (Assume the string does not slip and $g = 10 \ m/s^2$)